The stability of gold clusters doped with transition metal atoms (Sc, Ti, Cr, Fe) is studied with photofragmentation spectroscopy. The recorded stability patterns depend on the kind and the amount of dopants. While for singly doped clusters phenomenological electronic shell-model interpretations are suitable, limits of this model are encountered for more complex systems containing multiple dopants. Density-functional theory calculations were carried out on singly doped Au5X+ systems (X=Au, Sc, Ti, Cr, Fe). The electron delocalization behavior suggested by the qualitative description given in [Neukermans et al., Phys. Rev. Lett. 90, 033401 (2003)] is supported by the calculated molecular-orbital patterns. Dopant dependent differences in atomization energy, atomic-orbital occupancies and local magnetic moments are addressed. Evidence is presented to show that the number of delocalized electrons not only depends on the kind and amount of constituting atoms but also on the shape of the cluster.